Common sense suggests that counterfactuals are capable of truth and falsity, and that their truth values depend on more than just the actual course of events. Projectivists, like Mackie, deny the first; reductivists, like Lewis, deny the second. I criticize Mackie's and Lewis's theories, thereby defending realism. There are parallel issues and positions concerning the other concepts of the natural necessity family. A realist theory may also have a positive part, consisting of an account of some of the conceptual relations within this family. I try to cast light on the counterfactual by postulating a relation of accessibility between possible worlds - accessibility at the 'point' at which an event occurs.